Slenderness Ratio of a Column Explained
(A) l × r
(B) l/r
(C) (l × r)²
(D) √(l/r)
The slenderness ratio of a column is defined as the effective length (l) of the column divided by its radius of gyration (r). It is a dimensionless quantity that indicates the propensity of a column to buckle under axial load. A higher slenderness ratio signifies a greater tendency for the column to buckle.
Key Concepts
The slenderness ratio is calculated as:
Slenderness Ratio = l / r
Where:
- l = Effective length of the column (in units of length, e.g., mm, cm)
- r = Radius of gyration (in units of length, e.g., mm, cm)
Radius of Gyration
The radius of gyration (r) is a geometric property of a cross-section, calculated as:
r = √(I / A)
Where:
- I = Moment of inertia of the cross-sectional area (in units of length⁴, e.g., mm⁴, cm⁴)
- A = Cross-sectional area (in units of length², e.g., mm², cm²)
The radius of gyration represents the distance from the centroid of the cross-section at which the entire area can be assumed to be concentrated to produce the same moment of inertia. It measures how the area is distributed around the centroidal axis. A larger r indicates that the area is spread farther from the axis, increasing the column's resistance to buckling.
Summary Table
| Parameter | Description | Units |
|---|---|---|
| Slenderness Ratio (λ) | Effective length divided by radius of gyration (l/r) | Dimensionless |
| Effective Length (l) | Length of the column adjusted for end conditions | Length (e.g., mm, cm) |
| Radius of Gyration (r) | √(I/A), measures area distribution | Length (e.g., mm, cm) |
Key Notes
- The slenderness ratio is a critical factor in determining the buckling behavior of columns.
- A higher slenderness ratio increases the likelihood of buckling under compressive loads.
- The radius of gyration depends on the shape and size of the column’s cross-section.
- Units of the radius of gyration are in length (e.g., mm, cm), but the slenderness ratio is dimensionless.
Note: Understanding the slenderness ratio and radius of gyration is essential for designing stable columns in structural engineering.
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